Dirac, Majorana and Weyl fermions

TL;DR

This pedagogical article explains the definitions, motivations, and Lorentz group connections of Dirac, Majorana, and Weyl fermions, clarifying their relationships and the role of discrete symmetries like charge conjugation and CP.

Contribution

It provides a clear, pedagogical overview of fermion fields, emphasizing their Lorentz group properties and clarifying misconceptions about discrete symmetries.

Findings

Clarified the connection between fermion types and Lorentz group representations

Explained the role of charge conjugation and CP in Majorana fermions

Highlighted that definitions depend on Lorentz symmetry, not discrete symmetries

Abstract

This is a pedagogical article which discusses various kinds of fermion fields: Dirac, Majorana and Weyl. The definitions and motivations for introducing each kind of fields is discussed, along with the connections between them. It is pointed out that these definitions have to do with the proper Lorentz group, and not with respect to any discrete symmetry. The relationship of discrete symmetries like charge conjugation and CP, particularly important for Majorana fermions, has also been clarified.